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A on simplicity criterion for finite groups

Published online by Cambridge University Press:  09 April 2009

Nita Bryce
Nita Bryce
Affiliation:
Monash University, Clayton, Victoria
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M. Suzuki [3] has proved the following theorem. Let G be a finite group which has an involution t such that C = CG(t) ≅ SL(2, q) and q odd. Then G has an abelian odd order normal subgroup A such that G = CA and C ∩ A = 〈1〉.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 10 , Issue 3-4 , November 1969 , pp. 359 - 362
Copyright
Copyright © Australian Mathematical Society 1969

References

[1]Baer, R., ‘Classes of finite groups and their properties’, Illinois J. of Math. 1 (1957), 115–187.CrossRefGoogle Scholar
[2]Glauberman, G., ‘Central elements in core-free groups’. J. of Algebra 4 (1966), 403–420.CrossRefGoogle Scholar
[3]Suzuki, M., ‘On finite groups with cyclic Sylow subgroups for all odd primes’, Amer. J. Math. 77 (1955), 657–691.CrossRefGoogle Scholar
[4]Zassenhaus, H., ‘Kennzeichnung endlicher linearen Gruppen als Permutationsgruppen’, Abh. Hamburg Math. Sem. 11 (1936), 17–40.CrossRefGoogle Scholar